Context. In 2007 we reported two comet-shaped sources in the vicinity of Sgr A* (0.8 and 3.4 projected distance), named X7 and X3. The symmetry axes of the two sources are aligned to within 5 • in the plane of the sky, and the tips of their bow shocks point towards Sgr A*. Our measurements show that the proper motion vectors of both features are pointing in directions more than 45 • away from the line that connects them with Sgr A*. This misalignment of the bow-shock symmetry axes and their proper motion vectors, combined with the high proper motion velocities of several 100 km s −1 , suggest that the bow shocks must be produced by an interaction with some external fast wind, possibly coming from Sgr A*, or from stars in its vicinity. Aims. We have developed a bow-shock model to fit the observed morphology and constrain the source of the external wind. Methods. The result of our modeling gives the best solution for bow-shock standoff distances for the two features, which allows us to estimate the velocity of the external wind, making certain that all likely stellar types of the bow-shock stars are considered. Results. We show that neither of the two bow shocks (one of which is clearly associated with a stellar source) can be produced by the influence of a stellar wind of a single mass-losing star in the central parsec. Instead, an outflow carrying a momentum comparable to the one contributed by the ensemble of the massive young stars can drive shock velocities capable of producing the observed comet-shaped features. We argue that a collimated outflow arising perpendicular to the plane of the clockwise rotating stars (CWS) can easily account for the two features and the mini-cavity. However, the collective wind from the CWS has a scale of >10 . The presence of a strong, mass-loaded outbound wind at projected distances from Sgr A* of <1 in fact agrees with models that predict a highly inefficient accretion onto the central black hole owing to a strongly radius dependent accretion flow.